Comptes Rendus
Analysis of a Drift-Diffusion-Schrödinger–Poisson model
Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1007-1012.

A Drift-Diffusion-Schrödinger–Poisson system is presented, which models the transport of a quasi bidimensional electron gas confined in a nanostructure. We prove the existence of a unique solution to this nonlinear system. The proof makes use of some a priori estimates due to the physical structure of the problem, and also involves the resolution of a quasistatic Schrödinger–Poisson system.

Nous présentons un système de Dérive-Diffusion-Schrödinger–Poisson qui décrit le transport d'un gaz d'électrons confiné dans une nanostructure. Nous montrons que ce système admet une unique solution. Cette preuve d'existence est obtenue à l'aide d'estimations a priori dues à la nature physique du problème et passe par la résolution d'un système quasistatique de Schrödinger–Poisson.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02612-2

Naoufel Ben Abdallah 1; Florian Méhats 1; Nicolas Vauchelet 2

1 Mathématiques pour l'industrie et la physique, UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, 31032 Toulouse cedex 4, France
2 École normale supérieure de Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, France
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     title = {Analysis of a {Drift-Diffusion-Schr\"odinger{\textendash}Poisson} model},
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Naoufel Ben Abdallah; Florian Méhats; Nicolas Vauchelet. Analysis of a Drift-Diffusion-Schrödinger–Poisson model. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1007-1012. doi : 10.1016/S1631-073X(02)02612-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02612-2/

[1] N. Ben Abdallah, F. Méhats, On a Vlasov–Schrödinger–Poisson system, submitted

[2] N. Ben Abdallah, F. Méhats, N. Vauchelet, in preparation

[3] H. Gajewski On existence, uniqueness and asymptotic behavior of solutions of the basic equations for carrier transport in semiconductors, Z. Angew. Math. Mech, Volume 65 (1985) no. 2, pp. 101-108

[4] O.A. Ladyzenskaja; V.A. Solonnikov; N.N. Ural'ceva Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monographs, American Mathematical Society, 1988

[5] P.A. Markowich; C.A. Ringhofer; C. Schmeiser Semiconductor Equations, Springer-Verlag, Vienna, 1990

[6] F. Nier A stationary Schrödinger–Poisson system arising from the modelling of electronic devices, Forum Math, Volume 2 (1990) no. 5, pp. 489-510

[7] J. Pöschel; E. Trubowitz Inverse Spectral Theory, Academic Press, 1987

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